title: Combined recipe for clinical target volume and planning target volume margins.
abstract: OBJECTIVE
  To develop a combined recipe for clinical target volume (CTV) and planning target volume (PTV) margins.
  
  
  METHODS
  A widely accepted PTV margin recipe is M(geo) = aΣ(geo) + bσ(geo), with Σ(geo) and σ(geo) standard deviations (SDs) representing systematic and random geometric uncertainties, respectively. On the basis of histopathology data of breast and lung tumors, we suggest describing the distribution of microscopic islets around the gross tumor volume (GTV) by a half-Gaussian with SD Σ(micro), yielding as possible CTV margin recipe: M(micro) = ƒ(N(i)) × Σ(micro), with N(i) the average number of microscopic islets per patient. To determine ƒ(N(i)), a computer model was developed that simulated radiation therapy of a spherical GTV with isotropic distribution of microscopic disease in a large group of virtual patients. The minimal margin that yielded D(min) <95% in maximally 10% of patients was calculated for various Σ(micro) and N(i). Because Σ(micro) is independent of Σ(geo), we propose they should be added quadratically, yielding for a combined GTV-to-PTV margin recipe: M(GTV-PTV) = √{[aΣ(geo)](2) + [ƒ(N(i))Σ(micro)](2)} + bσ(geo). This was validated by the computer model through numerous simultaneous simulations of microscopic and geometric uncertainties.
  
  
  RESULTS
  The margin factor ƒ(N(i)) in a relevant range of Σ(micro) and N(i) can be given by: ƒ(N(i)) = 1.4 + 0.8log(N(i)). Filling in the other factors found in our simulations (a = 2.1 and b = 0.8) yields for the combined recipe: M(GTV-PTV) = √({2.1Σ(geo)}(2) + {[1.4 + 0.8log(N(i))] × Σ(micro)}(2)) + 0.8σ(geo). The average margin difference between the simultaneous simulations and the above recipe was 0.2 ± 0.8 mm (1 SD). Calculating M(geo) and M(micro) separately and adding them linearly overestimated PTVs by on average 5 mm. Margin recipes based on tumor control probability (TCP) instead of D(min) criteria yielded similar results.
  
  
  CONCLUSIONS
  A general recipe for GTV-to-PTV margins is proposed, which shows that CTV and PTV margins should be added in quadrature instead of linearly.
authors.affiliation: Department of Radiation Oncology, Champalimaud Foundation, Lisboa, Portugal. Electronic address: joep.stroom@fundacaochampalimaud.pt.
authors.forename: Joep
authors.initials: J
authors.lastname: Stroom
authors.affiliation: Department of Radiology, University Medical Center Utrecht, Utrecht, The Netherlands.
authors.forename: Kenneth
authors.initials: K
authors.lastname: Gilhuijs
authors.affiliation: Department of Radiation Oncology, Champalimaud Foundation, Lisboa, Portugal.
authors.forename: Sandra
authors.initials: S
authors.lastname: Vieira
authors.affiliation: Department of Radiation Oncology, The Netherlands Cancer Institute, Amsterdam, The Netherlands.
authors.forename: Wei
authors.initials: W
authors.lastname: Chen
authors.affiliation: Department of Radiation Oncology, The Netherlands Cancer Institute, Amsterdam, The Netherlands.
authors.forename: Javier
authors.initials: J
authors.lastname: Salguero
authors.affiliation: Department of Radiation Oncology, Champalimaud Foundation, Lisboa, Portugal.
authors.forename: Elizabeth
authors.initials: E
authors.lastname: Moser
authors.affiliation: Department of Radiation Oncology, The Netherlands Cancer Institute, Amsterdam, The Netherlands.
authors.forename: Jan-Jakob
authors.initials: JJ
authors.lastname: Sonke
mesh_terms: D000465:Algorithms; D001943:Breast Neoplasms / Q000473:pathology / Q000532:radiotherapy; D003198:Computer Simulation; D005260:Female; D006801:Humans; D008175:Lung Neoplasms / Q000473:pathology / Q000532:radiotherapy; D009010:Monte Carlo Method; D018365:Neoplasm, Residual; D047368:Tumor Burden; D035501:Uncertainty